Answer
(a) -1
(b) -2
(c) does not exist
(d) 2
(e) 0
(f) does not exist
(g) 1
(h) 3
Work Step by Step
(a) Looking at the graph, you can see that as the function approaches t=0 from the left side, g(t) = -1
(b) As the function approaches t=0 from the right side g(t)= -2
(c) The limit does not exist because as t approaches 0 from both sides, g(t) from the right side $\ne$ g(t) from the left side.
(d) As the function approaches t=2 from the left side g(t)= 2
(e) As the function approaches t=2 from the right side g(t)= 0
(f) The limit does not exist because as t approaches 2 from both sides, g(t) from the right side $\ne$ g(t) from the left side.
(g) At t=2, g(t) = 1
(h) As the function approaches t=4 from both sides g(t)=3 from the right side AND the left side. Therefore, $\lim\limits_{t \to 4}$ = 3
